Birkhoff's theorem with \(\Lambda\)-term and Bertotti-Kasner space (Q1966769)

If a \(\Lambda\)-term is included, the usual generalization of Schwarzschild space is not the only possible spherically symmetric vacuum solution. Another is Bertotti-Kasner space, as has been noted before but not explicitly demonstrated. The purpose of this note is to reformulate the unicity theorem and to discuss the extra solution. Historically, the solution called Bertotti-Kasner space by the author, was already deduced in 1950 by \textit{H. Nariai} [On some static solutions of Einstein's gravitational field equations in a spherically symmetric case, Sci. Rep. Tôhoku Univ., Ser. I 34, 160-167 (1950) which has been reprinted in Gen. Relativ. Gravitation 31, 951-961 (1999)] together with a new introduction by A. Krasinski (see Zbl 0959.83009 below).